{ "cells": [ { "cell_type": "markdown", "id": "49bcb5b0-f19d-4b96-a5f1-e0ae30f66d8f", "metadata": {}, "source": [ "## Violating the Laws of Physics for Fun and Insight!\n", "### A cascade of reactions `A <-> B <-> C` , mostly in the forward direction\n", "### [PART 1](#impossible_1_part1) : the above, together with a PHYSICALLY-IMPOSSIBLE \"closing\" of the cycle with :\n", "#### `C <-> A`, *ALSO* mostly in the forward direction _(never mind the laws of thermodymics)!_\n", "### [PART 2](#impossible_1_part2) : restoring the law of physics (by letting `C <-> A` adjust its kinetics based on the energy difference.)\n", "\n", "All 1st-order kinetics. \n", "\n", "LAST REVISED: June 4, 2023" ] }, { "cell_type": "markdown", "id": "7ba9c24d-102a-4571-8207-c5766525774f", "metadata": {}, "source": [ "![Temporarily suspending the Laws of Physics](../../docs/impossible_1.png)" ] }, { "cell_type": "code", "execution_count": 1, "id": "d9efa3fd-e95d-4e1c-878a-81ae932b2709", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Added 'D:\\Docs\\- MY CODE\\BioSimulations\\life123-Win7' to sys.path\n" ] } ], "source": [ "import set_path # Importing this module will add the project's home directory to sys.path" ] }, { "cell_type": "code", "execution_count": 2, "id": "01bae555-3dcf-42c1-bddc-9477a37f49f8", "metadata": { "tags": [] }, "outputs": [], "source": [ "from experiments.get_notebook_info import get_notebook_basename\n", "\n", "from src.modules.reactions.reaction_data import ChemData as chem\n", "from src.modules.reactions.reaction_dynamics import ReactionDynamics\n", "from src.modules.numerical.numerical import Numerical as num\n", "\n", "import numpy as np\n", "import plotly.express as px\n", "import plotly.graph_objects as go\n", "from src.modules.visualization.graphic_log import GraphicLog" ] }, { "cell_type": "code", "execution_count": 3, "id": "cc53849f-351d-49e0-bfa8-22f8d8e22f8e", "metadata": { "tags": [] }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "-> Output will be LOGGED into the file 'impossible_1.log.htm'\n" ] } ], "source": [ "# Initialize the HTML logging\n", "log_file = get_notebook_basename() + \".log.htm\" # Use the notebook base filename for the log file\n", "\n", "# Set up the use of some specified graphic (Vue) components\n", "GraphicLog.config(filename=log_file,\n", " components=[\"vue_cytoscape_1\"],\n", " extra_js=\"https://cdnjs.cloudflare.com/ajax/libs/cytoscape/3.21.2/cytoscape.umd.js\")" ] }, { "cell_type": "markdown", "id": "d6d3ca49-589d-49b7-8424-37c7b01bcacf", "metadata": {}, "source": [ "### Initialize the system" ] }, { "cell_type": "code", "execution_count": 4, "id": "32edd4eb-556d-40d3-8f25-8e515b5beaae", "metadata": {}, "outputs": [], "source": [ "# Initialize the system\n", "chem_data = chem(names=[\"A\", \"B\", \"C\"])\n", "\n", "# Reaction A <-> B, mostly in forward direction (favored energetically)\n", "# Note: all reactions in this experiment have 1st-order kinetics for all species\n", "chem_data.add_reaction(reactants=\"A\", products=\"B\",\n", " forward_rate=9., reverse_rate=3.)\n", "\n", "# Reaction B <-> C, also favored energetically\n", "chem_data.add_reaction(reactants=\"B\", products=\"C\",\n", " forward_rate=8., reverse_rate=4.)" ] }, { "cell_type": "markdown", "id": "faa20450-8753-4d19-ad1c-0cad77e6d165", "metadata": {}, "source": [ "# Part 1 - \"Turning off the Laws of Physics\"!" ] }, { "cell_type": "code", "execution_count": 5, "id": "95927c4b-8c13-462e-85f6-5d6db3006da2", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 3 (at temp. 25 C)\n", "0: A <-> B (kF = 9 / kR = 3 / Delta_G = -2,723.41 / K = 3) | 1st order in all reactants & products\n", "1: B <-> C (kF = 8 / kR = 4 / Delta_G = -1,718.28 / K = 2) | 1st order in all reactants & products\n", "2: C <-> A (kF = 3 / kR = 2 / Delta_G = -1,005.13 / K = 1.5) | 1st order in all reactants & products\n", "[GRAPHIC ELEMENT SENT TO LOG FILE `impossible_1.log.htm`]\n" ] } ], "source": [ "# LET'S VIOLATE THE LAWS OF PHYSICS!\n", "# Reaction C <-> A, also mostly in forward direction - MAGICALLY GOING \"UPSTREAM\" from C, to the higher-energy level of \"A\"\n", "chem_data.add_reaction(reactants=\"C\" , products=\"A\",\n", " forward_rate=3., reverse_rate=2.) # PHYSICALLY IMPOSSIBLE! Future versions of Life123 may flag this!\n", "\n", "chem_data.describe_reactions()\n", "\n", "# Send the plot of the reaction network to the HTML log file\n", "graph_data = chem_data.prepare_graph_network()\n", "GraphicLog.export_plot(graph_data, \"vue_cytoscape_1\")" ] }, { "cell_type": "markdown", "id": "15abbc56-c39d-4bb9-b1f1-d3b9911c7749", "metadata": {}, "source": [ "# Notice the absurdity of the energy levels always going down, throughout the cycle (like in an Escher painting!)" ] }, { "cell_type": "markdown", "id": "1c04542a-aba7-466a-9ee8-a2f550c6ced2", "metadata": {}, "source": [ "![Energy levels always going down](../../docs/impossible_1b.jpg)" ] }, { "cell_type": "markdown", "id": "d1d0eabb-b5b1-4e15-846d-5e483a5a24a7", "metadata": {}, "source": [ "### Set the initial concentrations of all the chemicals" ] }, { "cell_type": "code", "execution_count": 6, "id": "e4ff6a84-f5d5-4645-9c56-d9e981c108df", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "{'A': 100.0, 'B': 0.0, 'C': 0.0}" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "initial_conc = {\"A\": 100., \"B\": 0., \"C\": 0.} \n", "initial_conc" ] }, { "cell_type": "code", "execution_count": 7, "id": "e80645d6-eb5b-4c78-8b46-ae126d2cb2cf", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SYSTEM STATE at Time t = 0:\n", "3 species:\n", " Species 0 (A). Conc: 100.0\n", " Species 1 (B). Conc: 0.0\n", " Species 2 (C). Conc: 0.0\n" ] } ], "source": [ "dynamics = ReactionDynamics(reaction_data=chem_data)\n", "dynamics.set_conc(conc=initial_conc, snapshot=True)\n", "dynamics.describe_state()" ] }, { "cell_type": "code", "execution_count": 8, "id": "50ddd8e3-58c6-41f8-b874-ddc9a1d64d30", "metadata": { "lines_to_next_cell": 2 }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "200 total step(s) taken\n" ] } ], "source": [ "dynamics.set_diagnostics() # To save diagnostic information about the call to single_compartment_react()\n", "\n", "dynamics.single_compartment_react(initial_step=0.01, target_end_time=2.0,\n", " variable_steps=False) # To avoid extra complexity, we're sticking to simple fixed-time steps" ] }, { "cell_type": "code", "execution_count": 9, "id": "68172367-1929-4eb2-9350-864eebebb7e1", "metadata": {}, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dynamics.plot_curves()" ] }, { "cell_type": "code", "execution_count": 10, "id": "fbf24a85-b152-4b24-b350-00bed12e7bb9", "metadata": {}, "outputs": [], "source": [ "# dynamics.explain_time_advance()\n", "\n", "# dynamics.get_history()" ] }, { "cell_type": "markdown", "id": "225e1cd9-8c48-4ed4-8510-268476bae0c0", "metadata": {}, "source": [ "### It might look like an equilibrium has been reached. But NOT! Verify the LACK of final equilibrium state:" ] }, { "cell_type": "code", "execution_count": 11, "id": "f13381bb-d635-4667-b28c-99497370bf27", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A <-> B\n", "Final concentrations: [B] = 33.81 ; [A] = 21.43\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 1.57778\n", " Formula used: [B] / [A]\n", "2. Ratio of forward/reverse reaction rates: 3.0\n", "Discrepancy between the two values: 47.41 %\n", "Reaction is NOT in equilibrium (not within 1% tolerance)\n", "\n", "B <-> C\n", "Final concentrations: [C] = 44.76 ; [B] = 33.81\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 1.32394\n", " Formula used: [C] / [B]\n", "2. Ratio of forward/reverse reaction rates: 2.0\n", "Discrepancy between the two values: 33.8 %\n", "Reaction is NOT in equilibrium (not within 1% tolerance)\n", "\n", "C <-> A\n", "Final concentrations: [A] = 21.43 ; [C] = 44.76\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 0.478723\n", " Formula used: [A] / [C]\n", "2. Ratio of forward/reverse reaction rates: 1.5\n", "Discrepancy between the two values: 68.09 %\n", "Reaction is NOT in equilibrium (not within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "{False: [0, 1, 2]}" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.is_in_equilibrium()" ] }, { "cell_type": "markdown", "id": "f74cae99-4f86-4ce7-ad51-fff15ecdfa56", "metadata": {}, "source": [ "## Not surprisingly, none of the reactions of this physically-impossible hypothetical system are in equilibrium\n", "### Even though the concentrations don't change, it's NOT from equilibrium in the reactions - but rather from a balancing out of consuming and replenishing across reactions. \n", "#### Consider, for example, the concentrations of the chemical `A` at the end time, and contributions to its change (\"Delta A\") from the _individual_ reactions affecting `A`, as available from the diagnostic data:" ] }, { "cell_type": "code", "execution_count": 12, "id": "d3ef9936-020b-4ab3-b762-8a6cffb963b6", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Reaction: A <-> B\n" ] }, { "data": { "text/html": [ "
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START_TIMEDelta ADelta BDelta Ctime_stepcaption
1971.97-0.9142860.9142860.00.01
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" ], "text/plain": [ " START_TIME Delta A Delta B Delta C time_step caption\n", "197 1.97 -0.914286 0.914286 0.0 0.01 \n", "198 1.98 -0.914286 0.914286 0.0 0.01 \n", "199 1.99 -0.914286 0.914286 0.0 0.01 " ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_diagnostic_rxn_data(rxn_index=0, tail=3)" ] }, { "cell_type": "code", "execution_count": 13, "id": "1004ce75-b71b-4982-a68d-aa65cf8fcb1b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Reaction: C <-> A\n" ] }, { "data": { "text/html": [ "
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" ], "text/plain": [ " START_TIME Delta A Delta B Delta C time_step caption\n", "197 1.97 0.914286 0.0 -0.914286 0.01 \n", "198 1.98 0.914286 0.0 -0.914286 0.01 \n", "199 1.99 0.914286 0.0 -0.914286 0.01 " ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.get_diagnostic_rxn_data(rxn_index=2, tail=3)" ] }, { "cell_type": "markdown", "id": "f5b83b4d-f9be-4bd7-955f-803daa0bb658", "metadata": {}, "source": [ "### Looking at the last row from each of the 2 dataframes above, one case see that, at every reaction cycle, [A] gets reduced by some quantity (0.914286) by the reaction `A <-> B`, while simultaneously getting increased by the SAME amount by the (fictional) reaction `C <-> A`. \n", "### Hence, the concentration of A remains constant - but none of the reactions is in equilibrium!" ] }, { "cell_type": "code", "execution_count": null, "id": "1d51c42b-fcc0-47c8-9b84-122416b82f4a", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "d8cdc411-7b4d-4241-a218-9737f6cd2e0a", "metadata": {}, "source": [ "# PART 2 - Let's restore the Laws of Physics!" ] }, { "cell_type": "code", "execution_count": 14, "id": "e743e6a7-a8b1-4aba-b7db-4d7c61277a65", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 3 (at temp. 25 C)\n", "0: A <-> B (kF = 9 / kR = 3 / Delta_G = -2,723.41 / K = 3) | 1st order in all reactants & products\n", "1: B <-> C (kF = 8 / kR = 4 / Delta_G = -1,718.28 / K = 2) | 1st order in all reactants & products\n", "2: C <-> A (kF = 3 / kR = 2 / Delta_G = -1,005.13 / K = 1.5) | 1st order in all reactants & products\n" ] } ], "source": [ "chem_data.describe_reactions()" ] }, { "cell_type": "code", "execution_count": 15, "id": "f37675c8-827b-4c3d-bd55-93f776cc4989", "metadata": {}, "outputs": [], "source": [ "dynamics.clear_reactions() # Let's start over with the reactions (without affecting the data from the reactions)" ] }, { "cell_type": "code", "execution_count": 16, "id": "4d98c72b-986e-4122-9b2e-c4592b68d6fb", "metadata": {}, "outputs": [], "source": [ "# For the reactions A <-> B, and B <-> C, everything is being restored to the way it was before\n", "chem_data.add_reaction(reactants=\"A\", products=\"B\",\n", " forward_rate=9., reverse_rate=3.)\n", "\n", "# Reaction , also favored energetically\n", "chem_data.add_reaction(reactants=\"B\", products=\"C\",\n", " forward_rate=8., reverse_rate=4.)" ] }, { "cell_type": "code", "execution_count": 17, "id": "593bbaa1-bdf4-4bfd-a1ce-d0c843ca43f1", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 2 (at temp. 25 C)\n", "0: A <-> B (kF = 9 / kR = 3 / Delta_G = -2,723.41 / K = 3) | 1st order in all reactants & products\n", "1: B <-> C (kF = 8 / kR = 4 / Delta_G = -1,718.28 / K = 2) | 1st order in all reactants & products\n" ] } ], "source": [ "chem_data.describe_reactions()" ] }, { "cell_type": "code", "execution_count": 18, "id": "1e4e5e85-1407-440c-ba9c-dff59843b5ac", "metadata": {}, "outputs": [], "source": [ "# But for the reaction C <-> A, this time we'll \"bend the knee\" to the laws of thermodynamics!\n", "# We'll use the same forward rate as before, but we'll let the reverse rate be picked by the system, \n", "# based of thermodynamic data consistent with the previous 2 reactions : i.e. an energy difference of -(-2,723.41 - 1,718.28) = +4,441.69 (reflecting the \n", "# \"going uphill energetically\" from C to A\n", "chem_data.add_reaction(reactants=\"C\", products=\"A\",\n", " forward_rate=3., delta_G=4441.69) # Notice the positive Delta G: we're going from \"C\", to the higher-energy level of \"A\"" ] }, { "cell_type": "code", "execution_count": 19, "id": "707863ca-48d6-41b2-ad44-8fbce297cb4d", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of reactions: 3 (at temp. 25 C)\n", "0: A <-> B (kF = 9 / kR = 3 / Delta_G = -2,723.41 / K = 3) | 1st order in all reactants & products\n", "1: B <-> C (kF = 8 / kR = 4 / Delta_G = -1,718.28 / K = 2) | 1st order in all reactants & products\n", "2: C <-> A (kF = 3 / kR = 18 / Delta_G = 4,441.69 / K = 0.166667) | 1st order in all reactants & products\n" ] } ], "source": [ "chem_data.describe_reactions()" ] }, { "cell_type": "markdown", "id": "2fefd29d-ae6a-4eda-8a8f-81625a99bd30", "metadata": {}, "source": [ "# Notice how, now that we're again following the laws of thermodynamics, the last reaction is mostly IN REVERSE (low K < 1), as it ought to be! \n", "#### (considering how energetically unfavorable it is)" ] }, { "cell_type": "markdown", "id": "6f42feb3-f556-486b-bb8a-29a482ff4d2a", "metadata": {}, "source": [ "### Now, let's continue with this \"legit\" set of reactions, from where we left off in our fantasy world at time t=2:" ] }, { "cell_type": "code", "execution_count": 20, "id": "197dd1e8-9c3e-435a-8bb4-9b8f8cbda54b", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "400 total step(s) taken\n" ] } ], "source": [ "dynamics.single_compartment_react(initial_step=0.005, target_end_time=4.0,\n", " variable_steps=False)\n", "\n", "#dynamics.explain_time_advance()\n", "\n", "#dynamics.get_history()" ] }, { "cell_type": "code", "execution_count": 21, "id": "f06b91e6-730f-40cc-9566-cef4b16cb169", "metadata": {}, "outputs": [], "source": [ "fig0 = dynamics.plot_curves(suppress=True) # Prepare, but don't show, the main plot" ] }, { "cell_type": "code", "execution_count": 22, "id": "8d6ccc03-3e48-4142-bdbf-ca6d6fe6fda0", "metadata": {}, "outputs": [ { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "hovertemplate": "Chemical=A
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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Add a second plot, with a vertical gray line at t=2\n", "fig1 = px.line(x=[2,2], y=[0,100], color_discrete_sequence = ['gray'])\n", "\n", "# Combine the plots, and display them\n", "all_fig = go.Figure(data=fig0.data + fig1.data, layout = fig0.layout) # Note that the + is concatenating lists\n", "all_fig.update_layout(title=\"On the left of vertical gray line: FICTIONAL world; on the right: REAL world!\")\n", "all_fig.show()" ] }, { "cell_type": "markdown", "id": "2e79b987-135d-416d-baa3-797a5d0b56be", "metadata": {}, "source": [ "### Notice how [A] drops at time t=2, when we re-enact the Laws of Physics, because A no longer receives the extra boost from the previous mostly-forward (and thus physically-impossible given the unfavorable energy levels!) reaction `C <-> A`. \n", "### Back to the real world, that (energetically unfavored) reaction now mostly goes IN REVERSE; hence, the boost in [C] as well" ] }, { "cell_type": "markdown", "id": "c81944df-c125-4099-a81f-efc7ae0f9a6e", "metadata": {}, "source": [ "### Now, we have a REAL equilibrium!" ] }, { "cell_type": "code", "execution_count": 23, "id": "5dcb9571-340a-48a0-8711-f4d7ed6dcc0c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "A <-> B\n", "Final concentrations: [B] = 30 ; [A] = 10\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 3\n", " Formula used: [B] / [A]\n", "2. Ratio of forward/reverse reaction rates: 3.0\n", "Discrepancy between the two values: 9.469e-05 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n", "B <-> C\n", "Final concentrations: [C] = 60 ; [B] = 30\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 2\n", " Formula used: [C] / [B]\n", "2. Ratio of forward/reverse reaction rates: 2.0\n", "Discrepancy between the two values: 3.551e-05 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n", "C <-> A\n", "Final concentrations: [A] = 10 ; [C] = 60\n", "1. Ratio of reactant/product concentrations, adjusted for reaction orders: 0.166667\n", " Formula used: [A] / [C]\n", "2. Ratio of forward/reverse reaction rates: 0.16666696258266173\n", "Discrepancy between the two values: 4.735e-05 %\n", "Reaction IS in equilibrium (within 1% tolerance)\n", "\n" ] }, { "data": { "text/plain": [ "True" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "dynamics.is_in_equilibrium()" ] }, { "cell_type": "markdown", "id": "605b7936-546b-4b0c-bf33-cc5007e5343c", "metadata": {}, "source": [ "### The fact that individual reactions are now in actual, real equilibrium, can be easily seen from the last rows in the diagnostic data. Notice all the delta-concentration values at the final times are virtually zero:" ] }, { "cell_type": "code", "execution_count": 24, "id": "51b6568d-dbbb-4655-9f41-0b1ecc5a18da", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Reaction: A <-> B\n" ] }, { "data": { "text/html": [ "
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